Really cool! It gets really addicting once you get the engine going.
There was a weird difficulty curve, in that it's sort of inverted? E.g. the 2x2 grid is basically the most difficult (I keep getting into deadlocks seemingly without any way of avoiding it. But once I got past to the 4x4 grid, it got more manageable.
I enjoyed the extra additions to the original three types -- that was cool. The controls and UI was also really clear and good looking. Nicely done!